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gbg_data.txt
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gbg_data.txt
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Instructions for entering your graph braid group data:
1. Navigate to the empty template in this file below the dotted line.
2. Enter the number of particles/strands in your braid group.
3. Enter the adjacency matrix of your graph, following the guidelines below:
- First, make sure your graph does not contain any loops or multi-edges.
- Additionally, if your graph braid group has n particles:
-- Make sure all cycles in your graph have length at least n+1.
-- Make sure all paths between vertices of degree not equal to 1 have length at least n-1.
(Not doing the above two steps will produce computations for RB_n(\Gamma) instead of B_n(\Gamma).)
- Now, EITHER:
-- Enter each row of the matrix on a new line.
-- Separate each column with a single space.
- OR:
-- Write the matrix on a single line, enclosing it with square brackets and separating rows with commas.
-- Enclose each row with square brackets and separate the row's entries with commas.
(Tip: You can hand-draw your graph [here](https://www.mas.ncl.ac.uk/graph-curvature/) to easily get an adjacency matrix of the second form.
The adjacency matrix can be found in the bottom-left corner of the webpage.)
4. Enter an initial configuration for your particles, following the guidelines below:
- Enter the row numbers (in the adjacency matrix) of the vertices of the graph that your particles start at.
- Separate each number with a space.
- Row numbering begins at 1.
- If your graph is connected, this can be left blank.
Example 1:
Number of particles: 3
Adjacency matrix:
0 1 1 0 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 0 0
0 0 1 0 0 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 1 0 0 0
0 0 0 0 0 0 1 0 0 1 0 0
0 0 0 0 0 0 1 0 0 1 0 0
0 0 0 0 0 0 0 1 1 0 0 1
0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 1 1 0
Initial configuration: 2 4 12
Example 2:
Number of particles: 3
Adjacency matrix:
[[0,1,1,0,0,0,0,0,0,0,0,0],[1,0,0,1,0,0,0,0,0,0,0,0],[1,0,0,1,1,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,1,0,0,0],[0,0,0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,1,1,0]]
Initial configuration: 2 4 12
Please enter your data below the dotted line.
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Number of particles:
Adjacency matrix:
Initial configuration: